For the year 2000, there were an estimated 9 million new osteoporotic fractures, of which 1.6 million were at the hip, 1.7 million were at the forearm and 1.4 million were clinical vertebral fractures [1]. In clinical routine, osteoporosis diagnosis is largely based on the analysis of planar images obtained by Dual-energy X-ray Absorptiometry [2]. However, direct measurements performed using DXA projections are not able to accurately quantify the bone strength and predict an individual's risk of fracture. In particular, the cortical bone anatomical distribution is a critical component in determining the resistance of a bone to fracture [3] and cannot be evaluated using direct measurements in the 2D DXA projection. Physicians have to rely on 3D imaging techniques, such as Computed Tomography (CT), Quantitative Computed Tomography (QCT) or Magnetic Resonance Imaging (MRI). QCT uses a standard X-rays CT scanner together with a calibration phantom to convert Hounsfield Units of the CT images to Bone Mineral Density (BMD) values. Those techniques generate a set of slices containing information about the cortical bone. To overcome some of the limitations associated with CT, QCT or MRI devices (radiation dose and/or low availability for osteoporosis diagnosis in clinical environment), methods were recently proposed to reconstruct in 3D bony structures from 2D DXA projections [4, 5]. Similar to CT, QCT and MRI, the reconstructed 3D volume contains information about the cortical bone.
Measuring the cortical bone thickness and density from such 3D volumes or slices is not trivial. The cortical layer can be relatively thin in comparison with the image resolution, and previous studies have shown that straightforward measurement techniques of the cortical thickness and density such as the full-width half-maximum (FWHM) method [6] become inaccurate when measuring cortical thicknesses below around 3 mm. Many anatomical regions of interest for fracture risk assessment (femoral head, femoral neck, greater trochanter or vertebral body) exhibits cortical thicknesses below 3 mm.
Model-based estimation methods for measuring the cortex are capable of superior accuracy. Pakdel et al [7] performed the fitting of a function of the cortical thickness and density, image blur and surrounding tissue densities to actual CT data. However, this inverse problem is ill-posed, and several studies demonstrated that parameters of the function should be constrained to guarantee accurate results. Steekstra et al [8] proposed to study the point spread function of the CT device to constrain the image blur. This process requires a phantom to be scanned, which would modify current clinical routine practices. Treece et al [9, 10, 13] proposed to hold the parameter determining the cortical density at a constraining value during the fitting process. Assuming the cortical density to be constant is however not realistic, as several studies observed a trend for cortical density to increase with thickness. In later work, Treece et al [11] accounted for this trend by modelling the cortical density as a piecewise function of the thickness. Searching for the optimal value for constraining the cortical density [9, 10, 13] or the optimal parameters of the thickness-density piecewise function [11] require a region of thick cortex (above around 3 mm) to be present in the CT-scans. This is however not always the case, for example if only the upper part of the proximal femur (femoral head, neck and greater trochanter) is scanned. In addition, those algorithms require additional calculation steps to obtain an accurate estimation of the constraining density value or the thickness-density piecewise function, which complicated the overall process. Incorporating a constraining density value [10] requires to perform twice the fitting of a function at each node of the surface of the bone, while the algorithm relying on the thickness-density piecewise function [11] requires five iterations. There is therefore a need for improved techniques for estimating the cortical thickness and density, in particular when only regions of thin cortex are present in the medical images.